Time-series analysis of measurements on living cells illustrated by analysis of particle movement in the cytoplasm of tomato root hairs

Summary

Within a given root hair, the velocity of particle movement, here equated with “cytoplasmic streaming”, is usually very variable, making it difficult to distinguish experimentally-induced changes in velocity from those due to natural variability. Time-series analysis has been combined with piece-wise linear regression to provide an objective means of assessing the results of experiments in which the rate of streaming was recorded repeatedly from the same root hair. Ordinarily, regression and analysis of variance assume that the values in a data set are not strongly autocorrelated. These methods are applicable to sets of single observations (thus, they cannot be used with data obtained by repeated sampling of the same cell). By contrast, time-series analysis can take account of autocorrelations within the data and allows trends in the noise structure to be separated from treatment effects. The statistical methods described in the present paper are illustrated using the results from experiments in which the effect of α-naphthalene acetic acid on streaming velocity in tomato root hairs was recorded. The conclusions reached are in accord with published accounts of variation in protoplasmic streaming and the known behaviour of cells in response to auxins. Our results also provide an explanation for the failure of some workers to observe any consistent changes in streaming velocity in response to exogenous auxin. The method described makes use of well documented statistical techniques and could be applied to other investigations in which sequential measurements of quantifiable parameters, such as fluorometric determination of intracellular pH or concentrations of calcium, are made on intact living cells.